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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "ground/notation/relations/predicate_t_1.ma".
16 include "ground/relocation/pr_pat.ma".
18 (* TOTALITY CONDITION FOR PARTIAL RELOCATION MAPS ***************************)
21 definition pr_ist: predicate pr_map ≝
22 λf. ∀i. ∃j. @❨i,f❩ ≘ j.
25 "totality condition (partial relocation maps)"
26 'PredicateT f = (pr_ist f).
28 (* Basic inversions *********************************************************)
30 (*** istot_inv_push *)
31 lemma pr_ist_inv_push (g): 𝐓❨g❩ → ∀f. ⫯f = g → 𝐓❨f❩.
32 #g #Hg #f #H #i elim (Hg (↑i)) -Hg
33 #j #Hg elim (pr_pat_inv_succ_push … Hg … H) -Hg -H /2 width=3 by ex_intro/
36 (*** istot_inv_next *)
37 lemma pr_ist_inv_next (g): 𝐓❨g❩ → ∀f. ↑f = g → 𝐓❨f❩.
38 #g #Hg #f #H #i elim (Hg i) -Hg
39 #j #Hg elim (pr_pat_inv_next … Hg … H) -Hg -H /2 width=2 by ex_intro/
42 (* Basic constructions ******************************************************)
44 lemma pr_ist_push (f): 𝐓❨f❩ → 𝐓❨⫯f❩.
46 [ /3 width=2 by pr_pat_refl, ex_intro/
47 | #i elim (Hf i) -Hf /3 width=8 by pr_pat_push, ex_intro/
51 lemma pr_ist_next (f): 𝐓❨f❩ → 𝐓❨↑f❩.
52 #f #Hf #i elim (Hf i) -Hf
53 /3 width=6 by pr_pat_next, ex_intro/
56 (* Constructions with pr_tl *************************************************)
59 lemma pr_ist_tl (f): 𝐓❨f❩ → 𝐓❨⫰f❩.
60 #f cases (pr_map_split_tl f) *
61 /2 width=3 by pr_ist_inv_next, pr_ist_inv_push/